Multi-level,multi-objective optimization in process engineering

This paper presents a method for feasible decomposition applicable to large-scale, non-linear, multi-objective problems. The method, comprising a multi-level problem formulation and an interactive algorithm, has distinct advantages for dealing with real-world multi-objective optimization which is carried out by hierarchically arranged units of decision-making. The method is illustrated by its application to the optimal design of a water use and treatment process system.     

Simultaneous optimization and solution of systems described by differential/algebraic equations

Engineering approaches to the solution of constrained variational problems often involve converting the problem into a nonlinear programming (NLP) problem and solving it using current NLP methods. These methods usually use a sequential optimization and solution strategy. We propose a method, using piecewise constant functions for the independent variables, that combines the technologies of quasi-Newton optimization algorithms and global spline collocation to simultaneously optimize and integrate systems described by differential/algebraic equations. A computer implementable algorithm is discussed and three test problems are solved. The algorithm allows the solution of a more general class of optimization problems than previous methods employing this strategy.     

Robust supply chain performance via Model Predictive Control

This paper presents a novel robust Model Predictive Control (MPC) method for real-time supply chain optimization under uncertainties. This method optimizes the closed-loop economic performance of supply chain systems and addresses different sources of uncertainties located external to and within the feedback loop. The future system behavior is predicted by a closed-loop model, which includes both the open-loop system model and a controller model described by an optimization problem. The robust MPC formulation involves the solution of a constrained, bi-level stochastic optimization problem, which is transformed into a tractable problem involving a limited number of deterministic conic optimization problems solved reliably using an interior point method. The robust controller is applied to a real industrial multi-echelon supply chain optimization problem, and its performance is shown to reduce stock-outs without excessive inventories.     

Prior detection of genetic algorithm significant parameters: Coupling factorial design technique to genetic algorithm

This work presents an extension of a previous proposed procedure [Costa, C.B.B., Wolf Maciel, M.R., Maciel Filho, R., 2005. Factorial design technique applied to genetic algorithm parameters in a batch cooling crystallization optimization. Computers and Chemical Engineering 29, 2229-2241] to be adopted as a prior analysis in optimization problems to be solved using genetic algorithm (GA). Chemical engineering problems are commonly highly non-linear and possess a large number of variables, sometimes with significant interactions among them. Such characteristics make the optimization problems really difficult to be solved by deterministic methods. GA is an increasing tool for solving this sort of problems. However, no systematic approach to establish the best set of GA parameters for any problem was found in the literature and a relatively easy to use and meaningful approach is proposed and proved to be of general application. The proposed approach consists of applying factorial design, a well-established statistical technique to identify the most meaningful information about the influences of factors on a specific problem, as a support tool to identify the GA parameters with significant effect on the optimization problem. This approach is very useful in conducting further optimization works, since it discharges GA parameters that are not statistically significant for the evolutionary search for the optimum, saving time and computation burden in evolutionary optimization studies.     

Optimal robust optimization approximation for chance constrained optimization problem

Chance constraints are useful for modeling solution reliability in optimization under uncertainty. In general, solving chance constrained optimization problems is challenging and the existing methods for solving a chance constrained optimization problem largely rely on solving an approximation problem. Among the various approximation methods, robust optimization can provide safe and tractable analytical approximation. In this paper, we address the question of what is the optimal (least conservative) robust optimization approximation for the chance constrained optimization problems. A novel algorithm is proposed to find the smallest possible uncertainty set size that leads to the optimal robust optimization approximation. The proposed method first identifies the maximum set size that leads to feasible robust optimization problems and then identifies the best set size that leads to the desired probability of constraint satisfaction. Effectiveness of the proposed algorithm is demonstrated through a portfolio optimization problem, a production planning and a process scheduling problem.     

Global optimization of stiff dynamical systems

We present a deterministic global optimization method for nonlinear programming formulations constrained by stiff systems of ordinary differential equation (ODE) initial value problems (IVPs). The examples arise from dynamic optimization problems exhibiting both fast and slow transient phenomena commonly encountered in model-based systems engineering applications. The proposed approach utilizes unconditionally stable implicit integration methods to reformulate the ODE-constrained problem into a nonconvex nonlinear program (NLP) with implicit functions embedded. This problem is then solved to global optimality in finite time using a spatial branch-and-bound framework utilizing convex/concave relaxations of implicit functions constructed by a method which fully exploits problem sparsity. The algorithms were implemented in the Julia programming language within the EAGO.jl package and demonstrated on five illustrative examples with varying complexity relevant in process systems engineering. The developed methods enable the guaranteed global solution of dynamic optimization problems with stiff ODE–IVPs embedded.     

基于神经网络模型的混沌优化及其应用

研究一种新型优化算法－混沌优化,提出加快解的疏敛速度和精度新方法,并与精确不可微罚函数结合来求解非线性约束优化问题。对不能用数学解析式精确表达的优化问题利用神经网络建模,在此基础上进行混沌搜索寻优。该方法应用于甲醛生产过程的稳态优化,获得较好的经济效益。     

Numerical solution approaches for robust nonlinear optimal control problems

Nonlinear equality and inequality constrained optimization problems with uncertain parameters can be addressed by a robust worst-case formulation that leads to a bi-level min–max optimization problem. We propose and investigate a numerical method to solve this min–max optimization problem exactly in the case that the underlying maximization problem always has its solution on the boundary of the uncertainty set. This is an adoption of the local reduction approach used to solve generalized semi-infinite programs. The approach formulates an equilibrium constraint employing first order derivatives of both the uncertainty set and the user defined constraints. We propose two different ways for computation of these derivatives, one similar to the forward mode, the other similar to the reverse mode of automatic differentiation. We show the equivalence of the proposed approach to a method based on geometric considerations that was recently developed by some of the authors. We show how to generalize the techniques to optimal control problems. The robust dynamic optimization of a batch distillation illustrates that both techniques are numerically efficient and able to overcome the inexactness of another recently proposed numerical approach to address uncertainty in optimal control problems.     

OPTIMIZATION OF PROCESS CONDITIONS IN GAS-ASSISTED INJECTION MOLDING

Gas-assisted injection molding has been widely used to provide promising solutions to problems in conventional molding. With additional process parameters introduced, optimization in gas-assisted injection molding is much more complex than in conventional injection molding. This paper proposes an automated design methodology for gas-assisted injection molding with robustness in consideration. By introducing a definition of gas penetration cost, the optimization problems dealing with multiple quality issues can be modeled as constrained optimization problems, with the gas penetration cost as main objective function and other quality quantities as constraints. A direct search-based optimization procedure, the Complex method, is used to optimize a bounded single-criterion problem. To illustrate the proposed methodology, a case study is carried out on simulation results.     

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through integrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.     

An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units

The demand for fast solution of nonlinear optimization problems, coupled with the emergence of new concurrent computing architectures, drives the need for parallel algorithms to solve challenging nonlinear programming (NLP) problems. In this paper, we propose an augmented Lagrangian interior-point approach for general NLP problems that solves in parallel on a Graphics processing unit (GPU). The algorithm is iterative at three levels. The first level replaces the original problem by a sequence of bound-constrained optimization problems using an augmented Lagrangian method. Each of these bound-constrained problems is solved using a nonlinear interior-point method. Inside the interior-point method, the barrier sub-problems are solved using a variation of Newton's method, where the linear system is solved using a preconditioned conjugate gradient (PCG) method, which is implemented efficiently on a GPU in parallel. This algorithm shows an order of magnitude speedup on several test problems from the COPS test set.     

A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions

This study introduces the logic-based discrete-Benders decomposition (LD-BD) for Generalized Disjunctive Programming (GDP) superstructure problems with ordered Boolean variables. The key idea is to obtain Benders cuts that use neighborhood information of a reformulated version of Boolean variables. These Benders cuts are iteratively refined, which guarantees convergence to a local optimum. A mathematical case study, the optimization of a network with Continuous Stirred-Tank Reactors (CSTRs) in series, and a large-scale problem involving the design of a distillation column are considered to demonstrate the features of LD-BD. The results from these case studies have shown that the LD-BD method exhibited good performance by finding attractive locally optimal solutions relative to existing logic-based solvers for GDP problems. Based on these tests, the LD-BD method is a promising strategy to solve optimal synthesis problems with ordered discrete decisions emerging in chemical engineering applications.     

Parametric optimization with uncertainty on the left hand side of linear programs

Although parametric optimization with uncertainties on the objective function (OF) or on the so-called “right-hand-side” (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra.     

自适应混合粒子群约束优化算法及其在软测量模型参数估计中的应用

对于软测量模型参数估计问题, 针对传统梯度法求解非线性最小二乘模型时依赖初值、需要追加趋势分析进行验证和无法直接求解复杂问题的缺陷, 提出将参数估计化为约束优化问题, 使用混合优化算法求解的新思路。为此提出一种自适应混合粒子群约束优化算法(AHPSO-C)。在AHPSO-C算法中, 为平衡全局搜索(混沌粒子群)和局部搜索(内点法), 引入自适应内点法最大函数评价次数更新策略。对12个经典测试函数的仿真结果表明, AHPSO-C是求解约束优化问题的一种有效算法。将算法用于淤浆法高密度聚乙烯(HDPE)串级反应过程中熔融指数软测量模型参数估计, 验证了方法的可行性与优越性。     

炼厂生产计划优化模型

This article addresses a production planning optimization problem of overall refinery. The authors formulated the optimization problem as mixed integer linear programming. The model considers the main factors for optimizing the production plan of overall refinery related to the use of run-modes of processing units. The aim of this planning is to decide which run-mode to use in each processing unit in each period of a given horizon, to satisfy the demand, such as the total cost of production and inventory is minimized. The resulting model can be regarded as a generalized lot-sizing problem where a run-mode can produce and consume more than one product. The resulting optimization problem is large-sized and NP-hard. The authors have proposed a column generation-based algorithm called branch-and-price （BP） for solving the interested optimization problem. The model and implementation of the algorithm are described in detail in this article. The computational results verify the effectiveness of the proposed model and the solution method.     

Using functional programming to recognize named structure in an optimization problem: Application to pooling

Branch‐and‐cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially‐relevant nonconvex nonlinear Pooling Problem within a mixed‐integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3085–3095, 2016     

Real-Time Optimization Using Machine Learning Models Applied to the 4,4′-Diphenylmethane Diisocyanate Production Process

In this work, the optimal time-varying allocation of steam in a large-scale industrial isocyanate production process is addressed. This is a problem that falls into the category of real-time optimization (RTO). The application of RTO in practice faces two problems: First the available rigorous process models may not be suitable for use in real-time connected to the process. Second, there is always a mismatch between the predictions of the model and the behavior of the real plant. We address the first problem by training a neural net model as a surrogate to data generated by a rigorous simulation model so that the model is simple to implement and short execution times result. The second problem is tackled by adapting the optimization problem based on measured data such that convergence to the optimal operating conditions for the real plant is achieved.     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.     

Chemical Composition Determination at the Bottom Region of a Recovery Boiler Furnace by Direct Minimization of Gibbs Free Energy

An optimization strategy has been applied to describe the chemical composition at the furnace bottom in the Kraft recovery boiler of a pulp production process. The concentrations of each involved chemical species were calculated through an optimization approach, minimizing the Gibbs free energy of the system. Various systems were proposed and tested, assuming different chemical species and phases number. Because serious initialization problems were found at this stage for some of the proposed systems, an optimization heuristic method (PSO) was used for the first approach to the problem. Once the appropriate phases number and chemical species in the system were determined, the initialization problems disappeared and the use of a deterministic optimization method (SQP) became viable. The proposed approach has shown to be satisfactory to reproduce industrial data and also data reported in the open scientific literature.     

模式识别法在化工调优中的应用

模式识别调优的基本出发点是,以工艺参数为特征变量构筑模式空间,按调优目标划分样本的类别.采用模式特征抽提方法压缩工艺参数,找出影响目标的主要因素.分别对两类调优问题,即最优指标问题和最优方向问题,提出了寻找最优工况的具体处理方法.对多目标调优也作了简单的讨论.